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Full text of "Text Book Of Mechanical Engineering"

Appendix VI.

1091

The product of polar distance by intercept is an easier method
of finding a moment, because the former can be fixed artificially
as 10, or some simple multiple thereof.

This proof will also serve for the Culmann bending moment
diagram, pp. 446 and 885.

Problem. To draw a link polygon which shall pass through
three given points in the space diagram.

As the practical application is to cases of vertical and
parallel forces, such case only will be here considered. Re-

ferring to Fig. 964: let A B c be the given points, and D, E, F, G,
and H the given forces. The latter are set down in magnitude
and direction as o i, 12, 2 3, 3 4, and 4 5 on the vector figure.

1.  Firstly, make no attempt to pass through the points, but
choose any pole d and draw the polygon hfg.

2.  Take the two links Oi and 03 immediately over A and B
and produce them to find the resultant a b.   The same pair of
links in any other polygon would have the same resultant, for the
pole can be chosen anywhere.

3.  Take any point d, join to A and B and produce, forming
two such links in a new polygon.